Blender 2.8 - Can't select hair in point select mode in particle edit
I was able to look at this some more and it's only an issue in the blend file I was working with. The point select mode works as expected in brand new files.

I originally created the file in 2.79, perhaps that's part of the cause?

I can append everything from the old file into a new file and everything works, so I am going to go with that as my solution. But I'll keep the old files around and maybe file a bug report.